Can I remove weights/vertex groups for specific vertices?
Remove vert(s) from vertex group.

In edit mode, select the verts you want removed from group. Click the remove button on the Vertex Groups Edit Panel to remove from the active group.

Here is a sample where all the vertices of the default cube are added to the "Group" group.  The bottom face is selected and its verts removed from the group.  I've turned on the show weights in the mesh display panel to make visualizing the group easier.